OpenRaiser/Intern-Atlas huggingface dataset:
The Cost of Perfection for Matchings in Graphs
Venue: arXiv cs.DM 2014
Year: 2014

Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the computer graphics application in triangle meshes, where we seek to convert a triangulation into a quadrangulation by merging pairs of adjacent triangles, we focus mainly on bridgeless cubic graphs. First, we characterize graphs that attain the extreme ratios. Second, we present a lower bound for all bridgeless cubic graphs. Third, we present upper bounds for subclasses of bridgeless cubic graphs, most of which are shown to be tight. Additionally, we present tight bounds for the class of regular bipartite graphs.
Efficient sub-5 approximations for minimum dominating sets in unit disk graphs
Venue: arXiv cs.DS 2014
Year: 2014

A unit disk graph is the intersection graph of n congruent disks in the plane. Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks. Because the minimum dominating set problem for unit disk graphs is NP-hard, numerous approximation algorithms have been proposed in the literature, including some PTAS. However, since the proposal of a linear-time 5-approximation algorithm in 1995, the lack of efficient algorithms attaining better approximation factors has aroused attention. We introduce a linear-time O(n+m) approximation algorithm that takes the usual adjacency representation of the graph as input and outputs a 44/9-approximation. This approximation factor is also attained by a second algorithm, which takes the geometric representation of the graph as input and runs in O(n log n) time regardless of the number of edges. Additionally, we propose a 43/9-approximation which can be obtained in O(n^2 m) time given only the graph's adjacency representation. It is noteworthy that the dominating sets obtained by our algorithms are also independent sets.
Robust Estimates of Covariance Matrices in the Large Dimensional Regime
Venue: arXiv cs.IT 2014
Year: 2014

This article studies the limiting behavior of a class of robust population covariance matrix estimators, originally due to Maronna in 1976, in the regime where both the number of available samples and the population size grow large. Using tools from random matrix theory, we prove that, for sample vectors made of independent entries having some moment conditions, the difference between the sample covariance matrix and (a scaled version of) such robust estimator tends to zero in spectral norm, almost surely. This result can be applied to various statistical methods arising from random matrix theory that can be made robust without altering their first order behavior.
Citations, Sequence Alignments, Contagion, and Semantics: On Acyclic Structures and their Randomness
Venue: arXiv cs.DM 2014
Year: 2014

Datasets from several domains, such as life-sciences, semantic web, machine learning, natural language processing, etc. are naturally structured as acyclic graphs. These datasets, particularly those in bio-informatics and computational epidemiology, have grown tremendously over the last decade or so. Increasingly, as a consequence, there is a need to build and evaluate various strategies for processing acyclic structured graphs. Most of the proposed research models the real world acyclic structures as random graphs, i.e., they are generated by randomly selecting a subset of edges from all possible edges. Unfortunately the graphs thus generated have predictable and degenerate structures, i.e., the resulting graphs will always have almost the same degree distribution and very short paths. Specifically, we show that if $O(n \log n \log n)$ edges are added to a binary tree of $n$ nodes then with probability more than $O(1/(\log n)^{1/n})$ the depth of all but $O({\log \log n} ^{\log \log n})$ vertices of the dag collapses to 1. Experiments show that irregularity, as measured by distribution of length of random walks from root to leaves, is also predictable and small. The degree distribution and random walk length properties of real world graphs from these domains are significantly different from random graphs of similar vertex and edge size.
MacWilliams Identities for $m$-tuple Weight Enumerators
Venue: arXiv cs.IT 2014
Year: 2014

Since MacWilliams proved the original identity relating the Hamming weight enumerator of a linear code to the weight enumerator of its dual code there have been many different generalizations, leading to the development of $m$-tuple support enumerators. We prove a generalization of theorems of Britz and of Ray-Chaudhuri and Siap, which build on earlier work of Kløve, Shiromoto, Wan, and others. We then give illustrations of these $m$-tuple weight enumerators.
Complex-Demand Knapsack Problems and Incentives in AC Power Systems
Venue: arXiv cs.DS 2014
Year: 2014

We consider AC electrical systems where each electrical device has a power demand expressed as a complex number, and there is a limit on the magnitude of total power supply. Motivated by this scenario, we introduce the complex-demand knapsack problem (C-KP), a new variation of the traditional knapsack problem, where each item is associated with a demand as a complex number, rather than a real number often interpreted as weight or size of the item. While keeping the same goal as to maximize the sum of values of the selected items, we put the capacity limit on the magnitude of the sum of satisfied demands. For C-KP, we prove its inapproximability by FPTAS (unless P = NP), as well as presenting a (1/2-epsilon)-approximation algorithm. Furthermore, we investigate the selfish multi-agent setting where each agent is in charge of one item, and an agent may misreport the demand and value of his item for his own interest. We show a simple way to adapt our approximation algorithm to be monotone, which is sufficient for the existence of incentive compatible payments such that no agent has an incentive to misreport. Our results shed insight on the design of multi-agent systems for smart grid.
On the Minimum/Stopping Distance of Array Low-Density Parity-Check Codes
Venue: arXiv cs.IT 2014
Year: 2014

In this work, we study the minimum/stopping distance of array low-density parity-check (LDPC) codes. An array LDPC code is a quasi-cyclic LDPC code specified by two integers q and m, where q is an odd prime and m <= q. In the literature, the minimum/stopping distance of these codes (denoted by d(q,m) and h(q,m), respectively) has been thoroughly studied for m <= 5. Both exact results, for small values of q and m, and general (i.e., independent of q) bounds have been established. For m=6, the best known minimum distance upper bound, derived by Mittelholzer (IEEE Int. Symp. Inf. Theory, Jun./Jul. 2002), is d(q,6) <= 32. In this work, we derive an improved upper bound of d(q,6) <= 20 and a new upper bound d(q,7) <= 24 by using the concept of a template support matrix of a codeword/stopping set. The bounds are tight with high probability in the sense that we have not been able to find codewords of strictly lower weight for several values of q using a minimum distance probabilistic algorithm. Finally, we provide new specific minimum/stopping distance results for m <= 7 and low-to-moderate values of q <= 79.
kLog: A Language for Logical and Relational Learning with Kernels
Venue: arXiv cs.AI 2014
Year: 2014

We introduce kLog, a novel approach to statistical relational learning. Unlike standard approaches, kLog does not represent a probability distribution directly. It is rather a language to perform kernel-based learning on expressive logical and relational representations. kLog allows users to specify learning problems declaratively. It builds on simple but powerful concepts: learning from interpretations, entity/relationship data modeling, logic programming, and deductive databases. Access by the kernel to the rich representation is mediated by a technique we call graphicalization: the relational representation is first transformed into a graph --- in particular, a grounded entity/relationship diagram. Subsequently, a choice of graph kernel defines the feature space. kLog supports mixed numerical and symbolic data, as well as background knowledge in the form of Prolog or Datalog programs as in inductive logic programming systems. The kLog framework can be applied to tackle the same range of tasks that has made statistical relational learning so popular, including classification, regression, multitask learning, and collective classification. We also report about empirical comparisons, showing that kLog can be either more accurate, or much faster at the same level of accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at http://klog.dinfo.unifi.it along with tutorials.
Decision Taking as a Service
Venue: arXiv cs.SE 2014
Year: 2014

Decision taking can be performed as a service to other parties and it is amenable to outtasking rather than to outsourcing. Outtasking decision taking is compatible with selfsourcing of decision making activities carried out in preparation of decision taking. Decision taking as a service (DTaaS) is viewed as an instance of so-called decision casting. Preconditions for service casting are examined, and compliance of decision taking with these preconditions is confirmed. Potential advantages and disadvantages of using decision taking as a service are considered.
Hypercontractivity, Sum-of-Squares Proofs, and their Applications
Venue: arXiv cs.CC 2014
Year: 2014

We study the computational complexity of approximating the 2->q norm of linear operators (defined as ||A||_{2->q} = sup_v ||Av||_q/||v||_2), as well as connections between this question and issues arising in quantum information theory and the study of Khot's Unique Games Conjecture (UGC). We show the following: 1. For any constant even integer q>=4, a graph $G$ is a "small-set expander" if and only if the projector into the span of the top eigenvectors of G's adjacency matrix has bounded 2->q norm. As a corollary, a good approximation to the 2->q norm will refute the Small-Set Expansion Conjecture--a close variant of the UGC. We also show that such a good approximation can be obtained in exp(n^(2/q)) time, thus obtaining a different proof of the known subexponential algorithm for Small Set Expansion. 2. Constant rounds of the "Sum of Squares" semidefinite programing hierarchy certify an upper bound on the 2->4 norm of the projector to low-degree polynomials over the Boolean cube, as well certify the unsatisfiability of the "noisy cube" and "short code" based instances of Unique Games considered by prior works. This improves on the previous upper bound of exp(poly log n) rounds (for the "short code"), as well as separates the "Sum of Squares"/"Lasserre" hierarchy from weaker hierarchies that were known to require omega(1) rounds. 3. We show reductions between computing the 2->4 norm and computing the injective tensor norm of a tensor, a problem with connections to quantum information theory. Three corollaries are: (i) the 2->4 norm is NP-hard to approximate to precision inverse-polynomial in the dimension, (ii) the 2->4 norm does not have a good approximation (in the sense above) unless 3-SAT can be solved in time exp(sqrt(n) polylog(n)), and (iii) known algorithms for the quantum separability problem imply a non-trivial additive approximation for the 2->4 norm.
LDPC for QKD Reconciliation
Venue: arXiv cs.CR 2014
Year: 2014

We present the Low Density Parity Check (LDPC) forward error correction algorithm adapted for the Quantum Key Distribution (QKD) protocol in a form readily applied by developers. A sparse parity check matrix is required for the LDPC algorithm and we suggest using some that have been defined by the IEEE and ETSI standards organizations for use in various communication protocols. We evaluate the QKD performance of these various parity check matrices as a function of the quantum bit error rate. We also discuss the computational precision required for this LPDC algorithm. As QKD evolves towards deployment, complete algorithm descriptions and performance analysis, as we present, will be required.
On the Efficiency of Classical and Quantum Secure Function Evaluation
Venue: arXiv cs.CR 2014
Year: 2014

We provide bounds on the efficiency of secure one-sided output two-party computation of arbitrary finite functions from trusted distributed randomness in the statistical case. From these results we derive bounds on the efficiency of protocols that use different variants of OT as a black-box. When applied to implementations of OT, these bounds generalize most known results to the statistical case. Our results hold in particular for transformations between a finite number of primitives and for any error. In the second part we study the efficiency of quantum protocols implementing OT. While most classical lower bounds for perfectly secure reductions of OT to distributed randomness still hold in the quantum setting, we present a statistically secure protocol that violates these bounds by an arbitrarily large factor. We then prove a weaker lower bound that does hold in the statistical quantum setting and implies that even quantum protocols cannot extend OT. Finally, we present two lower bounds for reductions of OT to commitments and a protocol based on string commitments that is optimal with respect to both of these bounds.
On hybrid models of quantum finite automata
Venue: arXiv cs.FL 2014
Year: 2014

In the literature, there exist several quantum finite automata (QFA) models with both quantum and classical states. These models are of particular interest,as they show praiseworthy advantages over the fully quantum models in some nontrivial aspects. This paper characterizes these models in a uniform framework by proposing a general hybrid model consisting of a quantum component and a classical one which can interact with each other. The existing hybrid QFA can be naturally regarded as the general model with specific communication patterns (classical-quantum, quantum-classical, and two-way, respectively). We further clarify the relationship between these hybrid QFA and some other quantum models. In particular, it is shown that hybrid QFA can be simulated exactly by QFA with quantum operations, which in turn has a close relationship with two early proposed models: {\it ancialla QFA} and {\it quantum sequential machines}.
Parallel Discrete Event Simulation with Erlang
Venue: arXiv cs.DC 2014
Year: 2014

Discrete Event Simulation (DES) is a widely used technique in which the state of the simulator is updated by events happening at discrete points in time (hence the name). DES is used to model and analyze many kinds of systems, including computer architectures, communication networks, street traffic, and others. Parallel and Distributed Simulation (PADS) aims at improving the efficiency of DES by partitioning the simulation model across multiple processing elements, in order to enabling larger and/or more detailed studies to be carried out. The interest on PADS is increasing since the widespread availability of multicore processors and affordable high performance computing clusters. However, designing parallel simulation models requires considerable expertise, the result being that PADS techniques are not as widespread as they could be. In this paper we describe ErlangTW, a parallel simulation middleware based on the Time Warp synchronization protocol. ErlangTW is entirely written in Erlang, a concurrent, functional programming language specifically targeted at building distributed systems. We argue that writing parallel simulation models in Erlang is considerably easier than using conventional programming languages. Moreover, ErlangTW allows simulation models to be executed either on single-core, multicore and distributed computing architectures. We describe the design and prototype implementation of ErlangTW, and report some preliminary performance results on multicore and distributed architectures using the well known PHOLD benchmark.
Smoothed Functional Algorithms for Stochastic Optimization using q-Gaussian Distributions
Venue: arXiv cs.IT 2014
Year: 2014

Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, specially when the objective is to improve the performance of a stochastic system. However, the performance of these methods depends on several parameters, such as the choice of a suitable smoothing kernel. Different kernels have been studied in literature, which include Gaussian, Cauchy and uniform distributions among others. This paper studies a new class of kernels based on the q-Gaussian distribution, that has gained popularity in statistical physics over the last decade. Though the importance of this family of distributions is attributed to its ability to generalize the Gaussian distribution, we observe that this class encompasses almost all existing smoothing kernels. This motivates us to study SF schemes for gradient estimation using the q-Gaussian distribution. Using the derived gradient estimates, we propose two-timescale algorithms for optimization of a stochastic objective function in a constrained setting with projected gradient search approach. We prove the convergence of our algorithms to the set of stationary points of an associated ODE. We also demonstrate their performance numerically through simulations on a queuing model.
Constraint satisfaction parameterized by solution size
Venue: arXiv cs.CC 2014
Year: 2014

In the constraint satisfaction problem (CSP) corresponding to a constraint language (i.e., a set of relations) $Γ$, the goal is to find an assignment of values to variables so that a given set of constraints specified by relations from $Γ$ is satisfied. The complexity of this problem has received substantial amount of attention in the past decade. In this paper we study the fixed-parameter tractability of constraint satisfaction problems parameterized by the size of the solution in the following sense: one of the possible values, say 0, is "free," and the number of variables allowed to take other, "expensive," values is restricted. A size constraint requires that exactly $k$ variables take nonzero values. We also study a more refined version of this restriction: a global cardinality constraint prescribes how many variables have to be assigned each particular value. We study the parameterized complexity of these types of CSPs where the parameter is the required number $k$ of nonzero variables. As special cases, we can obtain natural and well-studied parameterized problems such as Independent Set, Vertex Cover, d-Hitting Set, Biclique, etc. In the case of constraint languages closed under substitution of constants, we give a complete characterization of the fixed-parameter tractable cases of CSPs with size constraints, and we show that all the remaining problems are W[1]-hard. For CSPs with cardinality constraints, we obtain a similar classification, but for some of the problems we are only able to show that they are Biclique-hard. The exact parameterized complexity of the Biclique problem is a notorious open problem, although it is believed to be W[1]-hard.
Asynchronous Multi-Tape Automata Intersection: Undecidability and Approximation
Venue: arXiv cs.LO 2014
Year: 2014

When their reading heads are allowed to move completely asynchronously, finite-state automata with multiple tapes achieve a significant expressive power, but also lose useful closure properties---closure under intersection, in particular. This paper investigates to what extent it is still feasible to use multi-tape automata as recognizer of polyadic predicates on words. On the negative side, determining whether the intersection of asynchronous multi-tape automata is expressible is not even semidecidable. On the positive side, we present an algorithm that computes under-approximations of the intersection; and discuss simple conditions under which it can construct complete intersections. A prototype implementation and a few non-trivial examples demonstrate the algorithm in practice.
Representation Learning: A Review and New Perspectives
Venue: arXiv cs.LG 2014
Year: 2014

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning.
Minimum KL-divergence on complements of $L_1$ balls
Venue: arXiv cs.IT 2014
Year: 2014

Pinsker's widely used inequality upper-bounds the total variation distance $||P-Q||_1$ in terms of the Kullback-Leibler divergence $D(P||Q)$. Although in general a bound in the reverse direction is impossible, in many applications the quantity of interest is actually $D^*(P,\eps)$ --- defined, for an arbitrary fixed $P$, as the infimum of $D(P||Q)$ over all distributions $Q$ that are $\eps$-far away from $P$ in total variation. We show that $D^*(P,\eps)\le C\eps^2 + O(\eps^3)$, where $C=C(P)=1/2$ for "balanced" distributions, thereby providing a kind of reverse Pinsker inequality. An application to large deviations is given, and some of the structural results may be of independent interest. Keywords: Pinsker inequality, Sanov's theorem, large deviations
Parameterized Complexity of Induced Graph Matching on Claw-Free Graphs
Venue: arXiv cs.DM 2014
Year: 2014

The Induced Graph Matching problem asks to find k disjoint induced subgraphs isomorphic to a given graph H in a given graph G such that there are no edges between vertices of different subgraphs. This problem generalizes the classical Independent Set and Induced Matching problems, among several other problems. We show that Induced Graph Matching is fixed-parameter tractable in k on claw-free graphs when H is a fixed connected graph, and even admits a polynomial kernel when H is a complete graph. Both results rely on a new, strong, and generic algorithmic structure theorem for claw-free graphs. Complementing the above positive results, we prove W[1]-hardness of Induced Graph Matching on graphs excluding K_1,4 as an induced subgraph, for any fixed complete graph H. In particular, we show that Independent Set is W[1]-hard on K_1,4-free graphs. Finally, we consider the complexity of Induced Graph Matching on a large subclass of claw-free graphs, namely on proper circular-arc graphs. We show that the problem is either polynomial-time solvable or NP-complete, depending on the connectivity of H and the structure of G.
The Capacity of More Capable Cognitive Interference Channels
Venue: arXiv cs.IT 2014
Year: 2014

We establish the capacity region for a class of discrete memoryless cognitive interference channel (DM-CIC) called cognitive-more-capable channel, and we show that superposition coding is the optimal encoding technique. This is the largest capacity region for the DM-CIC to date, as the existing capacity results are explicitly shown to be its subsets.